How can I render objects with very shiny surfaces?
What you are missing is proper lighting.

The main idea is that you are not photographing an object, but what is being reflected on it.

Ditch the HDR and start from scratch (Unless you have an HDR that reproduces a photographic studio used to photograph the exact same object from the exact point of view, any other HDR will be largely useless for what you want to do)

You have an object that is reflecting the environment around it.

Start by placing a very large plane with an emitter in the scene and see how is being reflected on the surface. Move it around the scene, and notice how the placement helps you reveal or not the shape and qualities of your object. Add a second emitter or just planes with a white surface. Find the correct placement for them. You need a mostly white environment around your object, but having gaps in between the emitters/reflectors will help you reveal the contours and subtle shapes of the object.

Look for websites on how to photograph shiny objects in the real world, there are a lot of them. The same techniques apply for 3D rendering.

This link might help: http://project52pros.com/2014pros/assignment-thirty-five-photographing-a-very-shiny-object/